Document FR-A-2 726 339 (see its FIGS. 13 to 15) describes an antivibration support of that type, in which the side wall of the elastomer body includes both two mutually opposite walls that are relatively slender and which constitute the above-mentioned slender portions, and two mutually opposite walls that are less slender and which constitute the above-mentioned support portions.
In that known antivibration support, the two slender walls contribute to diminishing the stiffness of the support, in particular against vibration at a relatively high frequency (greater than 20 Hz, e.g. in the vicinity of 150 Hz).
That phenomenon becomes even more marked when the slender walls are subjected to buckling by the support being loaded.
The antivibration support disclosed in the above-mentioned document provides satisfaction, however it nevertheless suffers from the drawback that the effects due to the flexibility of the slender walls, and in particular the buckling of said walls, are impeded by the fact that said slender walls are connected on either side to two relatively thick and rigid walls, constituting the support portions of the elastomer body.
That known antivibration support therefore does not make it possible to achieve complete independence in operation between the support portions of the elastomer body and the slender portions of the side wall of said elastomer body.